Name: Introduction to Mathematical Thinking
ISBN: 9780615653631

Introduction to Mathematical Thinking

"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.

What Hacker News says

calebjosueAug 2024

When Judea Pearl was asked how Mathematics should be taught, he answered: Chronollogicaly. [1]

Now, What do You mean to "learn Math". You have to be more specific with your goal. This is funny coming from me because I haven't able to specialize in any single topic.

Let's suppose You somehow saw The Beauty of Math somewhere and You are ready to continue your journey in such a beautiful topic.

I really believe You Will enjoy reading "Mathematics for The million" by Lancelot, I saw this recommended by Sir Anthony Hoare[2], You Will be amazed by its content (I have only ready chapter one).

What's Mathematics?

Are elementary school children doing Math when they solve addition and subtraction problems?

Is The High school student crunching mechanical procedures, plugging numbers into formulas doing Math?

Is theorem proving Math?

Daphne Koller said in an interview that we are all doing probabilistics when Thinking and making certain decisiones[3]. Are we all Mathematicians?

Do You want to study Math as a tool to help You in some other areas or study it itself as a subject?

It doesn't matter, You Will enjoy it and love it.

Trying yo answer your question. Learn some Arithmetic, just enough. Crunch some elementary algebra (in The fashion of Visualizing Algebra provided by Udacity). Read The book Geometry by Tatiana Alekseyevskaya, learn some Discrete Math (I recommend You the book on the topic by Thomas VanDrunnen), read the other four books in the gelfand series. Learn some logic. Read Introduction to Mathematical Thinking by Keith Devlin. I think at this point You Will able to read some resources o calculus or abstract Algebra.

If this seems like a Lot, don't dismay. There was this guy George Green having to take care of mill to make bread and do also found time for Mathematics, apparently DeMoivre was struggling financially. There people are just like You. Enjoy your Math journey

[1] The interview is available on Lex Fridman YouTube channel.

[2] The conversation between him and Leslie Lamport is available on YouTube

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ggr2342Jun 2023

For understanding higher math I have found this primer course extremely useful:

Introduction to Mathematical Thinking by Keith Devlin (Stanford) https://www.coursera.org/learn/mathematical-thinking

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adamgordonbellMay 2023

At some point I was interested in learning to read and write proofs.

I did the "Introduction to Mathematical Thinking" MOOC from Keith Devlin. The curriculum is available as a book as well.

The class is basically how to write and read proofs for non-math majors. It starts pretty slow, but gets harder at some point. The number theory proofs were fun.

You 'got to' grade others proofs online, and they graded yours which was an interesting way to get familiar with reading and writing proofs.

I recommend it because instead of an area of math it focuses on what it means to prove something. And the teacher is pretty entertaining.

https://www.amazon.ca/Introduction-Mathematical-Thinking-Kei...

https://www.coursera.org/learn/mathematical-thinking

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adamsmith143Jan 2023

A lot of comments about textbooks that helped in specific topics but I don't think that answers the spirit of OP's question. Sure working through ANY Linear Algebra textbook is going to improve your Linear Algebra skills.

In the spirit of OP's question:

How to Solve it by G. Polya

Solving Mathematical Problems by Terrence Tao

Introduction to Mathematical Thinking by Keith Devlin

Are all amazing, How to Solve it in particular is an all time classic.

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djmipsJan 2023

A lot of people have mentioned Keith Devlin's book "Introduction to Mathematical Thinking" by Keith Devlin but for me his other book "Mathematics: The Science of Patterns" was something that really had a huge impact on me just to put mathematics in perspective. Probably has something to do with my own personal character and education but I needed that perspective before I could take the next step. Then the "Introduction to Mathematical Thinking" is a great following read. So it depends where you are.

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jiriroJan 2023

Introduction to Mathematical Thinking by Keith Devlin

https://www.coursera.org/learn/mathematical-thinking?

This brought me what math is about:)

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